In my quest to secure and harden my system, I've been briefly researching disabling services in Linux; to my surprise, it would appear that in Ubuntu at least, services are disabled by default. Is the same the case in Linux Mint?

Linux Mint comes enabled with Samba to facilitate interoperability with Windows devices on your home network (like file and printer sharing). That is the only difference, as both Ubuntu and Linux Mint come with the avahi-daemon (for automatic discovery of network attached devices), cupsd (printing service), dhclient (to automatically get an IP address at boot) and dnsmasq (a local DNS forwarder, as part of NetworkManager) services running on a default install.

Both cupsd and dnsmasq by default only listen on localhost, so are never at risk. avahi-daemon and dhclient listen on the local network, so are not at risk on a home network. dhclient is needed on a public network (like a Wi-Fi hotspot) for DHCP to function, to get an IP address, so you wouldn't normally disable this service unless you have fixed IP address.

If you want you can disable Samba and Avahi if you don't need them. To shut both down until a reboot, run:

Yes, and if you have a broadband Internet connection your Cable/DSL modem would normally not allow remote users to connect to your machine in any case. Unless you configured that specifically. If you install or start additional services, and those are reachable from the Internet, you of course need to configure those properly for security. You can also enable the UFW firewall on Linux Mint easily, which will block all remote access to your services unless you configure to allow it.